Disorder enhanced quantum many-body scars in Hilbert crystals

TL;DR

This paper investigates how positional disorder in Rydberg chains enhances quantum many-body scars, linking many-body dynamics to single-particle behavior and revealing the robustness of certain scars against disorder.

Contribution

It introduces a Hilbert space topology approach to understand scars and demonstrates disorder-induced enhancement and localization effects in these systems.

Findings

Disorder enhances quantum many-body scars in Hilbert space.

Strong disorder leads to localization of eigenstates.

Mapping to spin chains clarifies the origin of certain scars' robustness.

Abstract

We consider a model arising in facilitated Rydberg chains with positional disorder which features a Hilbert space with the topology of a $d$-dimensional hypercube. This allows for a straightforward interpretation of the many-body dynamics in terms of a single particle one on the Hilbert space and provides an explicit link between the many-body and single particle scars. Exploiting this perspective, we show that an integrability-breaking disorder enhances the scars followed by inhibition of the dynamics due to strong localization of the eigenstates in the large disorder limit. Next, mapping the model to the spin-1/2 XX Heisenberg chain offers a simple geometrical perspective on the recently proposed Onsager scars [PRL ${\bf 124}$, 180604 (2020)], which can be identified with the scars on the edge of the Hilbert space. This makes apparent the origin of their insensitivity to certain types of disorder perturbations.